Question

.

Answer 1

you either have to run long hand or synthetic division ...

Answer 2

let x=2, do we get a zero? or a number?

Answer 3

its the same process as doing it for numbers .... but there is a simpler test

let x=2, what does the expression give us?

Answer 4

yes, this tells us that x-2 is not a factor and must have a remainder of -3/(x-2)

Answer 5

id pick the option that has a -3/(x-2) on it .....

Answer 6

youre welcome

a little insight into this wold be:

P(x) = (x-2) Q(x) + R

P(2) = (2-2) Q(2) + R = -3, R = -3

P(x) = (x-2) Q(x) - 3 , divide off the x-2
\[\frac{P(x)}{(x-2)}=Q(x)-\frac3{(x-2)}\]

Answer 7

regardless of the Q(x), the option we want has to have that -3/(x-2) tacked into it